If a matrix has 13 elements, then the possible dimensions (order) it can have are

Options

A. `1xx13,13xx1`
B. `1xx26,26xx1`
C. `2xx13,13xx2`
D. None of these

Answer

To determine the possible dimensions (order) of a matrix with 13 elements, we need to understand the relationship between the number of rows and columns in a matrix.

### Step-by-Step Solution:

1. **Understand the Definition of a Matrix**:
A matrix is defined by its dimensions, which are given as the number of rows (m) and the number of columns (n). The total number of elements in a matrix is given by the product of its dimensions, i.e., \( m \times n \).

2. **Set Up the Equation**:
Since the matrix has 13 elements, we can express this as:
\[ m \times n = 13 \]

3. **Identify the Factors of 13**:
The number 13 is a prime number, which means it has only two positive factors: 1 and 13. Therefore, the possible pairs of (m, n) that satisfy the equation \( m \times n = 13 \) are:
- \( (1, 13) \)
- \( (13, 1) \)

4. **List the Possible Dimensions**:
From the pairs identified, we can conclude that the possible dimensions (order) of the matrix are:
- 1 row and 13 columns (1 x 13)
- 13 rows and 1 column (13 x 1)

### Final Answer:
The possible dimensions (order) of a matrix with 13 elements are:
- \( 1 \times 13 \)
- \( 13 \times 1 \)